Question

The rate constant for the hydrolysis reaction of an ester by dilute acid is $0.6931\times {{10}^{-3}}$ ${{s}^{-1}}$. The time required to change the concentration of ester from 0.04M to 0.01M is-
(A) 6931s
(B) 4000s
(C) 2000s
(D) 1000s

Answer 1

Hint: To answer this question we should know about the order of the given reaction and the formula of rate constant in case of given order. By looking at the unit of the rate constant we can say that the reaction is a first order reaction.

Formula used will be:
 \[k\,=\,\dfrac{2.303}{t}\log \dfrac{a}{a-x}\]
Where, k is the rate constant and ‘t’ is the time taken

Complete step by step solution:
Let’s look at the answer of this question
It is given in the question that:
Rate constant (k) = $0.6931\times {{10}^{-3}}$ ${{s}^{-1}}$
Initial concentration (a) = 0.04M
Final concentration (a-x) = 0.01M
Now, from the units of the rate constants, we know that the given reaction is a first order reaction.
So using the formula,
\[k\,=\,\dfrac{2.303}{t}\log \dfrac{a}{a-x}\]
On putting the values given in the question, we get
\[t\,=\,\dfrac{2.303}{0.06931}\log \dfrac{0.04}{0.01}\]
\[t = 2000 sec\]
So, the required time is 2000sec
Hence, the answer for the given question is option (C).

Note: The units of rate constants depend on the order of the reactions. The formula for rate constant also varies with the order of the reactions.
In a first order reaction the rate of the reaction is dependent only on the concentration of one of the reactants.